Open AccessDynamics of Timoshenko system with time-varying weight and time-varying delay
Author(s) -
Carlos ato,
M. J. Dos Santos,
Carlos A. Raposo
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021053
Subject(s) - exponential stability , semigroup , exponential function , mathematics , exponential decay , stability (learning theory) , norm (philosophy) , exponential growth , mathematical analysis , control theory (sociology) , variable (mathematics) , physics , computer science , control (management) , quantum mechanics , nonlinear system , machine learning , artificial intelligence , nuclear physics , political science , law
This paper is concerned with the well-posedness of global solution and exponential stability to the Timoshenko system subject with time-varying weights and time-varying delay. We consider two problems: full and partially damped systems. We prove existence of global solution for both problems combining semigroup theory with the Kato's variable norm technique. To prove exponential stability, we apply the Energy Method. For partially damped system the exponential stability is proved under assumption of equal-speed wave propagation in the transversal and angular directions. For full damped system the exponential stability is obtained without the hypothesis of equal-speed wave propagation.